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 A196306 Coefficients of g.f. A(x) where -1 <= a(n) <= 1 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients. 3
 1, 3, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A(z) = 0 at z = -0.3218604126 5330206348 1666946119 2701743677 6909817084 3826086189 5315539535 3583969883 ... LINKS Paul D. Hanna, Table of n, a(n) for n = 0..1001 EXAMPLE G.f.: A(x) = 1 + 3*x + x^3 - x^6 - x^9 - x^12 - x^18 + x^21 - x^24 - x^30 - x^33 + x^39 - x^42 - x^45 + x^48 + x^54 - x^60 - x^66 - x^69 + x^72 - x^75 + x^84 - x^87 - x^90 - x^93 - x^96 - x^102 + x^108 - x^114 - x^126 + x^132 - x^135 - x^138 + x^141 - x^144 - x^147 - x^153 - x^159 - x^162 + x^165 - x^168 - x^171 + x^174 - x^180 - x^183 + x^186 - x^189 - x^192 + x^195 +... where A(x)^(1/3) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 9*x^5 - 22*x^6 + 55*x^7 - 142*x^8 + 375*x^9 - 1009*x^10 + 2753*x^11 - 7599*x^12 + 21178*x^13 - 59509*x^14 + 168401*x^15 - 479477*x^16 + 1372536*x^17 - 3947678*x^18 + 11402376*x^19 - 33059314*x^20 + 96177750*x^21 +...+ A196307(n)*x^n +... PROG (PARI) {a(n)=local(A=1+3*x); if(n==0, 1, if(n%3==0, for(j=1, n, for(k=-1, 1, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j); if(denominator(t)==1, A=A+k*x^j; break)))); polcoeff(A+x*O(x^n), n))} CROSSREFS Cf. A196307 (cube-root), A196308 (trisection); variants: A106216, A083953. Sequence in context: A271620 A098018 A260073 * A107093 A051830 A106216 Adjacent sequences:  A196303 A196304 A196305 * A196307 A196308 A196309 KEYWORD sign AUTHOR Paul D. Hanna, Oct 01 2011 STATUS approved

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Last modified September 21 00:14 EDT 2021. Contains 347596 sequences. (Running on oeis4.)